Question

What is the equation for this line

Answer 1

The equation of the line is $y=\frac{-1}{5} x-\frac{21}{5}$.

Solution:

The points on the line are (–6, –3) and (4, –5).

 $x_{1}=-6, y_{1}=-3, x_{2}=4, y_{2}=-5$

Slope of the line:

 $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

 $m=\frac{-5-(-3)}{4-(-6)}$

 $m=\frac{-5+3}{4+6}$

$m=\frac{-2}{10}$

$m=\frac{-1}{5}$

Point-slope formula:

 $y-y_{1}=m\left(x-x_{1}\right)$

 $y-(-3)=\frac{-1}{5}(x-(-6))$

 $y+3=\frac{-1}{5}(x+6)$

 $y+3=\frac{-1}{5} x-\frac{6}{5}$

Subtract 3 from both sides of the equation.

$y=\frac{-1}{5} x-\frac{21}{5}$

The equation of the line is  $y=\frac{-1}{5} x-\frac{21}{5}$.